CN117077298B - Aircraft robust optimization design method based on gradient enhancement random Co-Kriging model - Google Patents

Aircraft robust optimization design method based on gradient enhancement random Co-Kriging model Download PDF

Info

Publication number
CN117077298B
CN117077298B CN202311341946.XA CN202311341946A CN117077298B CN 117077298 B CN117077298 B CN 117077298B CN 202311341946 A CN202311341946 A CN 202311341946A CN 117077298 B CN117077298 B CN 117077298B
Authority
CN
China
Prior art keywords
gradient
design
response
aerodynamic
kriging model
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202311341946.XA
Other languages
Chinese (zh)
Other versions
CN117077298A (en
Inventor
王波
杨体浩
张健
应培
范景峰
高梓昂
张亚妮
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Institute of Engineering Thermophysics of CAS
Original Assignee
Institute of Engineering Thermophysics of CAS
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Institute of Engineering Thermophysics of CAS filed Critical Institute of Engineering Thermophysics of CAS
Priority to CN202311341946.XA priority Critical patent/CN117077298B/en
Publication of CN117077298A publication Critical patent/CN117077298A/en
Application granted granted Critical
Publication of CN117077298B publication Critical patent/CN117077298B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/27—Regression, e.g. linear or logistic regression
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/29—Graphical models, e.g. Bayesian networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/08—Probabilistic or stochastic CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/08—Fluids
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/28—Fuselage, exterior or interior
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • Data Mining & Analysis (AREA)
  • Computer Hardware Design (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Artificial Intelligence (AREA)
  • Software Systems (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Mathematical Optimization (AREA)
  • Evolutionary Biology (AREA)
  • Bioinformatics & Computational Biology (AREA)
  • Pure & Applied Mathematics (AREA)
  • Bioinformatics & Cheminformatics (AREA)
  • Mathematical Analysis (AREA)
  • Fluid Mechanics (AREA)
  • Medical Informatics (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Computer Graphics (AREA)
  • Automation & Control Theory (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Computing Systems (AREA)
  • Algebra (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a robust optimization design method of an aircraft based on a gradient enhancement random Co-Kriging model. Then, taking into account the uncertainty aerodynamic design variables, sampling in random space, and calculating its aerodynamic properties and its gradient information for the geometric design variables. Next, a gradient enhancement stochastic Co-Kriging model is constructed for uncertainty quantitative analysis. And finally, based on aerodynamic statistical moment and gradient information thereof, performing robust optimization by utilizing an SNOPT optimization algorithm until the algorithm converges.

Description

Aircraft robust optimization design method based on gradient enhancement random Co-Kriging model
Technical Field
The invention belongs to the technical field of aircraft aerodynamic design optimization, relates to a robust optimization design method of aircraft aerodynamic design, and in particular relates to a robust optimization design method of an aircraft based on a gradient-enhanced stochastic Co-Kriging model.
Background
Uncertainty quantification (Uncertainty Quantification, UQ) is a method for researching statistical characteristics and uncertainty propagation rules of a system under the influence of uncertainty factors, and can provide theoretical basis and technical support for reliability analysis, robust optimization design, risk assessment and the like of the system. In recent years, with the continuous and deep research on the uncertainty of CFD, the uncertainty of CFD is quantified, and the research on the propagation of the uncertainty under the influence of random factors is greatly paid attention. Uncertainty quantization methods can be classified into two types, i.e., embedded (Intruive) and Non-embedded (NI) methods, according to the coupling manner with the CFD solver. Compared with the embedded method, the non-embedded method can obtain the statistical characteristics under the uncertain conditions by adopting the existing solver, and does not need to modify a control equation and rewrite a program, and meanwhile, the risk of introducing new errors is greatly avoided.
The more viable solution strategies for NIUQ of CFD are mainly deterministic proxy model (DMBA) based and stochastic proxy model (SMBA) based approaches. Briefly, the DMBA method constructs a deterministic response surface based on known uncertainty information, and then performs statistical inference on the response surface. The SMBA method is a method for directly analyzing and processing the uncertainty problem through the mapping relation (namely, random proxy model) between random variables after the mapping relation is established for the input and output according to the known uncertainty information. Compared with DMBA, the SMBA has the characteristics of small calculated amount, strong pertinence of the adopted random agent model to the uncertainty problem, more reliable response statistical information and the like. One of the SMBA methods widely used in the UQ field is a random proxy model method based on Kriging theory. Kriging is an interpolation method based on a Gaussian process, which utilizes known input and output data to obtain a mean function and a covariance function of the Gaussian process through methods such as maximum likelihood estimation or Bayesian inference, so as to construct a proxy model capable of describing the input and output relation of an original system model. Kriging is considered to be a more accurate and robust method from the aspects of nonlinear description, high dimensional processing problems, and the like. The Stochastic Kriging stochastic proxy model (SK) developed by the Kriging theory further considers the uncertainty information of each input and output data point, and has a relatively excellent description capability due to the fact that the uncertainty problem of high space dimension and strong nonlinearity degree is concerned and applied widely.
Aircraft aerodynamic design is an important component of aircraft engineering that directly affects the performance and safety of an aircraft. In pneumatic design of an aircraft, in addition to performing UQ analysis, robust optimization design (Robust Aircraft Design Optimization, RADO) is required, that is, a set of optimal design variables are found in consideration of uncertainty influences (such as changes in design parameters, changes in environmental conditions, model errors, etc.), so that the aircraft has optimal objective function values on the premise of meeting various constraint conditions, and has strong robustness to uncertainty factors. The conventional aircraft pneumatic design method, such as the reverse design based on Euler CFD, the coupling based on a genetic algorithm and a reduced order method, the Euler CFD based on a pneumatic accompanying method and the like, generally has the characteristics of high dimensionality, high complexity, high nonlinearity and the like, so that the RADO method also faces the challenges of large calculation amount, low calculation efficiency and the like.
In combination with the background, aiming at the problems of large calculated amount, high dimension and strong nonlinearity of the pneumatic design of the aircraft, how to fully utilize the characteristics of high precision, high robustness, high reliability and the like of the SK proxy model in the optimal design process of the aircraft and establish a RADO method based on the characteristics, thereby effectively solving the problems of large calculated amount and low calculation efficiency in the robust optimization process of the aircraft.
Disclosure of Invention
Object of the invention
Aiming at the defects and shortcomings in the prior art, in order to solve the problems of large calculated amount, low calculation efficiency, high dimensionality, strong nonlinearity and the like in the pneumatic design robust optimization process of the existing aircraft, the invention fully utilizes the characteristics of high precision, high robustness, high reliability and the like of an SK proxy model, and provides a robust optimization design method based on a gradient enhanced random Co-Kriging model for the design work of the wing type, the wing and even the whole aircraft of the aircraft by constructing the random proxy model taking the gradient enhanced random Co-Kriging model as the background and establishing the robust optimization design method based on the model. The invention also verifies the practicability and feasibility of the constructed gradient optimization method through transonic airfoil calculation examples. The calculation example results show that the full turbulence robust optimization result obviously reduces the average value of the resistance coefficient under the condition that the robustness of the initial configuration is kept basically unchanged.
(II) technical scheme
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
the aircraft robust optimization design method based on the gradient enhancement stochastic Co-Kriging model is characterized by at least comprising the following steps of:
SS1, selecting an existing aircraft or a pneumatic component thereof as a basic sample point to be optimized, providing at least pneumatic appearance geometric data related to the basic sample point and deterministic pneumatic design conditions thereof, and setting design variables and constraint conditions related to stable optimization;
SS2, generating a grid set which corresponds to the aerodynamic shape of the basic sample point and can be used for CFD calculation and at least comprises a surface grid and a volume grid by using an FFD (Free-Form definition) geometric parameterization method and a IDW (Inverse Distance Weighting) dynamic grid technology based on the aerodynamic shape geometric data of the basic sample point;
SS3, sampling a basic sample point in random space by taking the uncertainty as a variable in combination with a given uncertainty variable statistical distribution characteristic in a given pneumatic design variable range to obtain a sample set which is matched with the modeling requirement of a gradient enhanced random Co-Kriging model and comprises a plurality of expansion sample points, wherein the number of the expansion sample points is consistent with that of the sampling points, and each expansion sample point comprises a geometric design variable and an uncertainty pneumatic design variable;
based on each expansion sample point which is generated in the step SS3 and contains the geometric design variable and the uncertainty pneumatic design variable, calculating the corresponding pneumatic characteristics one by utilizing a CFD numerical simulation method, and respectively calculating the gradient information of the pneumatic characteristics on the geometric design variable by utilizing a pneumatic coupling accompanying method to generate a sample set containing the pneumatic characteristics of each expansion sample point and the gradient information thereof;
SS5, constructing a gradient enhancement random Co-Kriging model aiming at each sample data point by utilizing the sample set generated in the step SS4, and carrying out uncertainty quantitative analysis to obtain aerodynamic statistical moment and gradient information of the statistical moment on geometric design variables;
SS6, based on the aerodynamic statistical moment and the gradient information of the statistical moment to the geometric design variable, which are obtained by the uncertainty quantitative analysis in the step SS5, taking the FFD control point as the geometric design variable and the aerodynamic statistical moment as the optimization target, and under the constraint condition given in the step SS1, performing aerodynamic robust optimization by using a SNOPT (Sparse Nonlinear OPTimizer) optimization algorithm based on the gradient;
and SS7, judging whether the SNOPT optimization algorithm is converged, if the SNOPT optimization algorithm is not converged, taking the new geometric design variable value obtained by optimizing in the step SS6 as a new basic sample point, repeating the steps SS 2-SS 6, and returning an optimization result after the SNOPT optimization algorithm is converged.
Preferably, in step SS1, the deterministic aerodynamic design condition includes at least a reynolds numberReMach numberMaAngle of attack for airflowαThe design variables include at least geometric design variables and aerodynamic design variables including an uncertainty amount, the aerodynamic design variables include at least Mach numbersMaAngle of attack of air flowαThe constraints at least comprise geometric constraints and pneumatic constraints.
Preferably, in step SS2, the FFD geometric parameterization method uses a bezier curve-based FFD method to flexibly control the aerodynamic profile of the aircraft or its aerodynamic components, and can reduce the number of control points and design variables required.
Preferably, in step SS2, the IDW dynamic grid technique is an IDW method based on a local coordinate system, so as to maintain the quality and orthogonality of the grids and avoid grid overlapping and grid degradation.
Preferably, in step SS2, the grid set includes at least a surface grid and a volume grid, and the surface grid and the volume grid each adopt a structured grid, an unstructured grid or a hybrid grid to adapt to different flow field characteristics and calculation requirements.
Preferably, in step SS3 above, for the basic sample points, the pneumatic design variables containing the uncertainty amount are sampled in random space using a uniform latin hypercube method (Latin Hypercube Sampling) that employs an optimization algorithm based on a maximum minimum distance criterion (MaximinDistance Criterion) to improve uniformity and representativeness of the sample points by maximizing the minimum distance between the sample points and avoid aggregation and nulling of the sample points.
Preferably, in step SS3, the geometric design variable in each of the extended sample points includes at least an FFD control point, and the uncertainty pneumatic design variable includes at least a mach numberMaAngle of attack of air flowα。
Preferably, in the step SS4, the pneumatic coupling adjoint method uses a discrete adjoint equation, and uses a control equation and a discrete format of a reynolds average numerical simulation (Reynolds average Navier-stocks, RANS) solver.
Preferably, in step SS4, the aerodynamic characteristics include at least a lift coefficient, a drag coefficient, and a moment coefficient, and the gradient information of the aerodynamic characteristics to the geometric design variable includes at least a gradient of the lift coefficient to the FFD control point coordinates, a gradient of the drag coefficient to the FFD control point coordinates, and a gradient of the moment coefficient to the FFD control point coordinates, and the moment coefficient includes at least a roll moment, a pitch moment, and a yaw moment.
Preferably, in the step SS5, a gradient enhancement stochastic Co-Kriging model is constructed at least based on the following sub-steps:
SS51. First through the Master responseYAndn p personal auxiliary responseW i To define a stochastic process associated with deterministic objective functions and gradients thereof, the principal responseYAnd each auxiliary responseW i Are all made of a mean functionμAnd a covariance functionZTo define GaussianThe process GP is as follows:
（1）
wherein,n p is a positive integer which is used for the preparation of the high-voltage power supply,Din the real number domain of the number,μ 0 、μ i respectively, main responsesYResponse aidW i Is used as a mean function of (a),Z 0 、Z i respectively, main responsesYResponse aidW i Covariance function x of (0) Is an input variable vector, andμ 0 、µ i all are of unknown constant and are of a constant,Z 0 is a function of the generalized distance between sample points,Z 0 all ofZ i A steady-state Gaussian random process with a mean value of 0;
SS52. In the specific case of gradient enhanced Co-Kriging model, the response will be aidedW i Modified to correspond to the primary responseYWith respect to input variablesx i The components of the gradient, namely:
（2）
a main response is availableYMean and variance of (a)Each auxiliary responseW i Mean and variance>The method comprises the following steps:
（3）
（4）
（5）
（6）
SS 53A general random Co-Kriging model of mean value is built by polynomial regression based on step SS52 and each auxiliary response is used to limit the number of inputs requiredW i Mean function of (2)μ i By responding to the masterYMean function of (2)µ 0 Obtained by differentiation of (a), namely:
（7）
（8）
wherein,
and wherein the first and second heat sinks are disposed,β j for the weight coefficient corresponding to the jth principal response component,ƒ j for the jth principal response component,n t the number of the main response components;
SS54 using master responseYAuxiliary responseW i The Best Linear Unbiased Predictor (BLUP) of the response of (1) constitutes a gradient-enhanced stochastic Co-Kriging model based on:
（9）
wherein,response prediction for using gradient enhanced stochastic Co-Kriging modelValue of->For each principal response component->Corresponding weight coefficient, ++>For each auxiliary response component->The corresponding weight coefficient is used for the weight of the object,n s the number of the main response components;
SS55 for the gradient enhanced random Co-Kriging model of equation (9) by minimizing the estimation error functionIs evaluated while taking into account unbiased conditions.
Further, in the above substep SS55, the unbiased condition based on the gradient enhanced random Co-Kriging model is:
（10）
further, bringing the formula (7) and the formula (8) into the formula (10) gives the following unbiased conditions:
（11）
wherein,，
，
，
。
further, equation (11) can be further simplified to:
（12）
wherein the vector isComprises->The co-ordinated kriging coefficient is used,is->A matrix.
Further, in the above substep SS55, the variance of the Co-Kriging error estimate is:
and the following symbols are introduced to simplify covariance:
（13）
the variance of the Co-Kriging gold error estimate written in matrix notation is obtained as follows:
（14）
wherein,is the covariance matrix of Jin Xie in the covariance matrix of KrigingArrayCCross-covariance matrix formed by covariance between primary and secondary responsesC WY Cross covariance matrix between auxiliary response and auxiliary responseC WW The composition, using the symbols introduced in equation (13), is defined as:
。
preferably, in step SS6, the SNOPT optimization algorithm adopts a method based on sequence quadratic programming (Sequential Quadratic Programming, SQP), uses gradient information provided by a gradient-enhanced stochastic Co-Kriging model to construct a quadratic programming sub-problem, and uses Trust Region (Trust Region) strategy to control the scale and solution accuracy of the sub-problem.
Preferably, in step SS6, the aerodynamic statistical momentDFor the target aerodynamic coefficientCThe mathematical expression of the linear combination of the mean and the standard deviation is as follows:
wherein,Kis a weight factor.
(III) technical effects
Compared with the prior art, the aircraft robust optimization design method based on the gradient enhancement random Co-Kriging model has the following beneficial and remarkable technical effects:
(1) According to the aircraft robust optimization design method based on the gradient enhancement random Co-Kriging model, by adopting the gradient enhancement random Co-Kriging proxy model, the aerodynamic characteristics of an aircraft or aerodynamic components thereof can be accurately fitted, and the gradient information of the aerodynamic characteristics on geometric design variables can be calculated by effectively utilizing a pneumatic coupling accompanying method, so that the accuracy and the robustness of the proxy model are improved, the calculated amount is reduced, the calculation efficiency of robust optimization of the aerodynamic design of the aircraft is remarkably improved, and a high-precision, high-robustness and high-reliability optimization scheme is provided for complex aircraft design.
(2) According to the aircraft robust optimization design method based on the gradient enhancement random Co-Kriging model, FFD control points are used as geometric design variables, aerodynamic statistical moment is used as an optimization target, and under given constraint conditions, the SNOPT optimization algorithm based on the gradient is used for pneumatic robust optimization. Compared with the traditional random sampling methods based on the Monte Carlo method or Latin hypercube sampling method and the like, the robust optimization design method can greatly reduce the number of samples and the calculated amount required by uncertainty research, and can accelerate convergence and improve the precision through gradient information.
(3) The aircraft robust optimization design method based on the gradient enhancement random Co-Kriging model adopts the grid generation method based on the FFD geometric parameterization method and the IDW dynamic grid technology, can flexibly control the aerodynamic appearance of the aircraft or the aerodynamic components thereof, can maintain the quality and the orthogonality of grids, and avoids the problems of grid overlapping, grid degradation and the like. Compared with the traditional geometric parameterization method based on polynomials or spline curves and the dynamic grid technology based on elasticity or springs, the grid generation method can better adapt to different flow field characteristics and calculation requirements, and can reduce the number of required control points and the number of design variables.
(4) The aircraft robust optimization design method based on the gradient enhancement random Co-Kriging model, provided by the invention, has the advantages that the practicability and feasibility are verified through transonic airfoil calculation, and the effect and stability of the method in practical application are ensured.
Drawings
FIG. 1 is a schematic diagram of an implementation flow of a robust optimization design method for an aircraft based on a gradient-enhanced stochastic Co-Kriging model;
FIG. 2 is a diagram of a mesh division of RAE 2822;
FIG. 3 is a schematic diagram of the aerodynamic geometry and FFD control frame of the airfoil RAE 2822;
FIG. 4 is a graph showing a random drag performance distribution of a robust optimization result of a transonic airfoil;
FIG. 5 is a graph showing airfoil results versus schematic in a transonic airfoil robust optimization result;
FIG. 6 is a graph showing a comparison of pressure distribution results in a transonic airfoil robust optimization result.
Detailed Description
For a better understanding of the present invention, the following examples are set forth to illustrate the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, embodiments of the invention. The embodiments described below by referring to the drawings are illustrative and intended to explain the present invention and should not be construed as limiting the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention. The following describes the structure and technical scheme of the present invention in detail with reference to the accompanying drawings, and an embodiment of the present invention is given.
As shown in FIG. 1, the aircraft robust optimization design method based on the gradient enhancement stochastic Co-Kriging model mainly comprises the following steps when in implementation:
and SS1, selecting an existing aircraft or a pneumatic component thereof as a basic sample point to be optimized, providing at least pneumatic appearance geometric data related to the basic sample point and deterministic pneumatic design conditions thereof, and setting design variables and constraint conditions related to stable optimization. The deterministic aerodynamic design conditions include at least a Reynolds numberReMach numberMaAngle of attack for airflowαThe design variables include at least geometric design variables and aerodynamic design variables including an uncertainty amount, the aerodynamic design variables include at least Mach numbersMaAngle of attack of air flowαThe constraints include at least geometric constraints and aerodynamic constraints.
And SS2, generating a grid set which corresponds to the aerodynamic shape of the basic sample point and can be used for CFD calculation and at least comprises a surface grid and a volume grid by using an FFD (Free-Form analysis) geometric parameterization method and a IDW (InverseDistance Weighting) dynamic grid technology based on the aerodynamic shape geometric data of the basic sample point. The FFD geometric parameterization method preferably adopts an FFD method based on Bezier curves so as to flexibly control the aerodynamic shape of the aircraft or aerodynamic components thereof and reduce the number of required control points and design variables. The IDW dynamic grid technique preferably employs an IDW method based on a local coordinate system to maintain grid quality and orthogonality and avoid grid overlap and grid degradation. The grid set at least comprises a surface grid and a volume grid, and the surface grid and the volume grid are structured grids, unstructured grids or mixed grids so as to adapt to different flow field characteristics and calculation requirements.
And SS3, for a basic sample point, sampling a pneumatic design variable containing uncertainty in a random space by taking the uncertainty as a variable in combination with a given uncertainty variable statistical distribution characteristic in a given pneumatic design variable range to obtain a sample set containing a plurality of extended sample points, wherein the number of the extended sample points is consistent with that of the sampling points, and each extended sample point contains a geometric design variable and an uncertainty pneumatic design variable, and the sample set is matched with the modeling requirement of a gradient enhanced random Co-Kriging model.
In a preferred example of the invention, for basic sample points, for pneumatic design variables containing an uncertainty amount, sampling is performed in random space using a uniform Latin hypercube method (Latin Hypercube Sampling) that employs an optimization algorithm based on a maximum minimum distance criterion (MaximinDistance Criterion) to improve uniformity and representativeness of sample points by maximizing minimum distances between sample points and avoid aggregation and nulling of sample points. The geometric design variable in each extended sample point at least comprises an FFD control point, and the uncertainty pneumatic design variable at least comprises Mach numberMaAngle of attack of air flowα。
And SS4, calculating the corresponding aerodynamic characteristics one by utilizing a CFD numerical simulation method based on each extended sample point which is generated in the step SS3 and contains the geometric design variable and the uncertainty aerodynamic design variable, and calculating the gradient information of the aerodynamic characteristics to the geometric design variable by utilizing an aerodynamic coupling accompanying method respectively to generate a sample set which contains the aerodynamic characteristics of each extended sample point and the gradient information thereof. The pneumatic coupling adjoint method preferably adopts a discrete adjoint equation, and utilizes a control equation and a discrete format of a Reynolds average numerical simulation solver. The aerodynamic characteristics at least comprise a lift coefficient, a drag coefficient and a moment coefficient, the gradient information of the aerodynamic characteristics on the geometric design variables at least comprises a gradient of the lift coefficient on FFD control point coordinates, a gradient of the drag coefficient on FFD control point coordinates and a gradient of the moment coefficient on FFD control point coordinates, and the moment coefficient at least comprises a rolling moment, a pitching moment and a yaw moment.
And SS5, constructing a gradient enhancement random Co-Kriging model for each sample data point by utilizing the sample set generated in the step SS4, and carrying out uncertainty quantitative analysis to obtain aerodynamic statistical moment and gradient information of the statistical moment on geometric design variables.
And SS6, based on aerodynamic statistical moment and gradient information of the statistical moment to the geometric design variable, which are obtained by uncertainty quantitative analysis in the step SS5, taking the FFD control point as the geometric design variable and the aerodynamic statistical moment as an optimization target, and performing aerodynamic robust optimization by using a gradient-based SNOPT (Sparse Nonlinear OPTimizer) optimization algorithm under the constraint condition given in the step SS1. The SNOPT optimization algorithm preferably adopts a sequence quadratic programming (Sequential Quadratic Programming, SQP) based method, utilizes gradient information provided by a gradient enhanced random Co-Kriging model to construct a quadratic programming sub-problem, and utilizes a trust region (TrustRegion) strategy to control the scale and solving accuracy of the sub-problem.
Aerodynamic statistical momentDFor the target aerodynamic coefficientCThe mathematical expression of the linear combination of the mean value and the standard deviation isWherein, the method comprises the steps of, wherein,Kis a weight factor.
And SS7, judging whether the SNOPT optimization algorithm is converged, if the SNOPT optimization algorithm is not converged, taking the new geometric design variable value obtained by optimizing in the step SS6 as a new basic sample point, repeating the steps SS 2-SS 6, and returning an optimization result after the SNOPT optimization algorithm is converged.
In the step SS5, a gradient enhancement random Co-Kriging model is constructed based on the following substeps:
SS51. First through the Master responseYAndn p personal auxiliary responseW i To define a stochastic process associated with deterministic objective functions and gradients thereof, the principal responseYAnd each auxiliary responseW i Are all made of a mean functionμAnd a covariance functionZA gaussian process GP defined, namely:
（1）
wherein,n p is a positive integer which is used for the preparation of the high-voltage power supply,Din the real number domain of the number,μ 0 、μ i respectively, main responsesYResponse aidW i Is used as a mean function of (a),Z 0 、Z i respectively, main responsesYResponse aidW i Covariance function x of (0) Is an input variable vector, andμ 0 、µ i all are of unknown constant and are of a constant,Z 0 is a function of the generalized distance between sample points,Z 0 all ofZ i A steady-state Gaussian random process with a mean value of 0;
SS52. In the specific case of gradient enhanced Co-Kriging model, the response will be aidedW i Modified to correspond to the primary responseYWith respect to input variablesx i The components of the gradient, namely:
（2）
a main response is availableYMean and variance of (a)Each auxiliary responseW i Mean and variance>The method comprises the following steps:
（3）
（4）
（5）
（6）
SS 53A general random Co-Kriging model of mean value is built by polynomial regression based on step SS52 and each auxiliary response is used to limit the number of inputs requiredW i Mean function of (2)μ i By responding to the masterYMean function of (2)µ 0 Obtained by differentiation of (a), namely:
（7）
（8）
wherein,
and wherein the first and second heat sinks are disposed,β j for the weight coefficient corresponding to the jth principal response component,ƒ j for the jth principal response component,n t the number of the main response components;
SS54 using master responseYAuxiliary responseW i The Best Linear Unbiased Predictor (BLUP) of the response of (1) constitutes a gradient-enhanced stochastic Co-Kriging model based on:
（9）
wherein,for response prediction values obtained using gradient enhanced stochastic Co-Kriging model, < + >>For each principal response component->Corresponding weight coefficient, ++>For each auxiliary response component->The corresponding weight coefficient is used for the weight of the object,n s the number of the main response components;
SS55 for the gradient enhanced random Co-Kriging model of equation (9) by minimizing the estimation error functionIs evaluated while taking into account the following unbiased conditions:
（10）
further, bringing the formula (7) and the formula (8) into the formula (10) gives the following unbiased conditions:
（11）
wherein,，/> ，/>
。
further, equation (11) can be further simplified to:
（12）
wherein the vector isComprises->The co-ordinated kriging coefficient is used,is->A matrix.
Further, in the above substep SS55, the variance of the Co-Kriging error estimate is:
/>
and the following symbols are introduced to simplify covariance:
（13）
the variance of the Co-Kriging gold error estimate written in matrix notation is obtained as follows:
（14）
wherein,is a covariance matrix of Jin Xie in covariance, which is a Kriging covariance matrixCCross-covariance matrix formed by covariance between primary and secondary responsesC WY Cross covariance matrix between auxiliary response and auxiliary responseC WW The composition, using the symbols introduced in equation (13), is defined as:
。
more specifically, the initial airfoil selection RAE2822, design state referenceHonda Jet，Ma=0.70，Re=7.93×10 6 ，C l =0.38, the airfoil mesh is shown in fig. 2, and the FFD control box is shown in fig. 3. Consideration of Mach number for the airfoilMaAnd angle of attackαAnd (5) uncertainty optimization design. The robust optimization problem is defined as shown in table 1 below. The total number of design variables in the optimization process is 16, and lift force constraint is set to be fixed lift forceC l Control low head moment to set moment constraint =0.38C mz Not less than-0.045, area constraintS≤S initial Thickness constraintt y ≤0.3t initial 。
In consideration of Mach numberMaAnd angle of attackαThe uncertainty of the total turbulence optimization assumes that Mach number and attack angle respectively satisfyNormal distribution and->The airfoil lift coefficient at this time in the mean state is 0.3. In the laminar flow optimization taking into account the uncertainty of Mach number and angle of attack, it is assumed that Mach number and angle of attack respectively satisfy +.>Normal distribution and->The airfoil lift coefficient at this time in the mean state is 0.3.
Table 2 gives the force coefficient results for a full turbulence robust optimization, where FTUMOpt (Full Turbulent Uncertainty Multiple factor Optimization) is the optimum design for full turbulence taking into account mach number and angle of attack uncertainty. It is known that the final drag reduction is 5.5counts, about 5.8% by full turbulence robust optimization design; wherein the pressure differential resistance is mainly reduced, while the frictional resistance remains almost unchanged.
And then, uncertainty analysis considering Mach number and attack angle is carried out on the Initial configuration, and comparison is carried out with a full turbulence steady optimization result, wherein the mean value and variance of the resistance coefficient are shown in table 3, and Initial-M represents the result of the Initial configuration under the influence of the Mach number and attack angle uncertainty. It is known that for the full turbulence optimization, the mean value of the drag coefficient is reduced by 5.53counts compared with the initial configuration, and the variance is basically unchanged.
And for the full turbulence robust optimization result, sampling in a random space by adopting a gradient enhanced random Co-Kriging model and carrying out uncertainty analysis, wherein the obtained random sample point resistance coefficient distribution is shown in figure 4. For a violin diagram, the upper and lower positions can approximately represent the height of the average value of the resistance coefficient, and the shape of the violin diagram represents the robustness of the resistance performance. It is known that the full turbulence robust optimization results significantly reduce the average value of the drag coefficient while keeping the initial configuration robustness substantially unchanged. This suggests that robust optimization can guarantee synchronous optimization in terms of average performance and performance robustness.
Fig. 5, 6 show a comparison of the results of the full turbulence robust optimization, wherein fig. 5 is the airfoil result and fig. 6 is the pressure distribution result. The radius of the head of the airfoil which is optimized in a steady way by the full turbulence is slightly increased, the position of the maximum thickness of the upper surface is moved forward, and the thickness of the lower surface is slightly reduced; the peak of the suction on the upper surface of the corresponding pressure distribution increases greatly.
The gradient enhancement Stochastic Co-Kriging method is used for carrying out application research of a robust optimization method considering multi-state uncertainty factors based on the existing work. The method can obtain global variance estimation based on the samples with uncertainty, and directly replaces numerical simulation after reaching a certain precision, so that the calculated amount based on uncertainty research is greatly reduced, and the important problem of uncertainty-based optimal design is solved.
The object of the present invention is fully effectively achieved by the above-described embodiments. Those skilled in the art will appreciate that the present invention includes, but is not limited to, those illustrated in the drawings and described in the foregoing detailed description. While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the scope of the appended claims.

Claims (15)

1. The aircraft robust optimization design method based on the gradient enhancement stochastic Co-Kriging model is characterized by at least comprising the following steps of:
SS1, selecting an existing aircraft or a pneumatic component thereof as a basic sample point to be optimized, providing at least pneumatic appearance geometric data related to the basic sample point and deterministic pneumatic design conditions thereof, and setting design variables and constraint conditions related to stable optimization;
SS2, generating a grid set which is used for CFD calculation and at least comprises a surface grid and a volume grid and corresponds to the aerodynamic shape of the basic sample point by utilizing an FFD geometric parameterization method and an IDW dynamic grid technology based on the aerodynamic shape geometric data of the basic sample point;
SS3, sampling a basic sample point in random space by taking the uncertainty as a variable in combination with a given uncertainty variable statistical distribution characteristic in a given pneumatic design variable range to obtain a sample set which is matched with the modeling requirement of a gradient enhanced random Co-Kriging model and comprises a plurality of expansion sample points, wherein the number of the expansion sample points is consistent with that of the sampling points, and each expansion sample point comprises a geometric design variable and an uncertainty pneumatic design variable;
based on each expansion sample point which is generated in the step SS3 and contains the geometric design variable and the uncertainty pneumatic design variable, calculating the corresponding pneumatic characteristics one by utilizing a CFD numerical simulation method, and respectively calculating the gradient information of the pneumatic characteristics on the geometric design variable by utilizing a pneumatic coupling accompanying method to generate a sample set containing the pneumatic characteristics of each expansion sample point and the gradient information thereof;
SS5, constructing a gradient enhancement stochastic Co-Kriging model for each sample data point by utilizing the sample set generated in the step SS4, and carrying out uncertainty quantitative analysis to obtain aerodynamic statistical moment and gradient information of the statistical moment on geometric design variables, wherein the gradient enhancement stochastic Co-Kriging model is constructed at least based on the following substeps:
SS51. First through the Master responseYAndn p personal auxiliary responseW i To define a stochastic process associated with deterministic objective functions and gradients thereof, the principal responseYAnd each auxiliary responseW i Are all made of a mean functionμAnd a covariance functionZTo define a gaussian process, namely:
（1）
wherein,n p is a positive integer which is used for the preparation of the high-voltage power supply,Din the real number domain of the number,μ 0 、μ i respectively, main responsesYResponse aidW i Is used as a mean function of (a),Z 0 、Z i respectively, main responsesYResponse aidW i Covariance function x of (0) Is an input variable vector, andμ 0 、μ i all are of unknown constant and are of a constant,Z 0 is a function of the generalized distance between sample points,Z 0 all ofZ i A steady-state Gaussian random process with a mean value of 0;
SS52. Auxiliary response under gradient enhanced Co-Kriging modelW i Modified to correspond to the primary responseYWith respect to input variablesx i The components of the gradient, namely:
（2）
obtaining a main responseYMean and variance of (a)Each auxiliary responseW i Mean and variance>The method comprises the following steps:
（3）
（4）
（5）
（6）
SS 53A general random Co-Kriging model of mean value is built by polynomial regression based on step SS52 and each auxiliary response is used to limit the number of inputs requiredW i Mean function of (2)μ i By responding to the masterYMean function of (2)μ 0 Obtained by differentiation of (a), namely:
（7）
（8）
wherein,
and wherein the first and second heat sinks are disposed,β j for the weight coefficient corresponding to the jth principal response component,f j for the jth principal response component,n t the number of the main response components;
SS54 using master responseYAuxiliary responseW i The best linear unbiased predictor of response of (c) constitutes a gradient-enhanced stochastic Co-Kriging model based on:
（9）
wherein,for response prediction values obtained using gradient enhanced stochastic Co-Kriging model, < + >>For each principal response component->Corresponding weight coefficient, ++>For each auxiliary response component->The corresponding weight coefficient is used for the weight of the object,n s the number of the main response components;
for the gradient enhancement random Co-Kriging model shown in formula (9), the error function is estimated by minimizingIs evaluated while taking into account unbiased conditions;
SS6, based on the aerodynamic statistical moment and the gradient information of the statistical moment to the geometric design variable, which are obtained by the uncertainty quantitative analysis in the step SS5, taking the FFD control point as the geometric design variable and the aerodynamic statistical moment as the optimization target, and under the constraint condition given in the step SS1, performing pneumatic robust optimization by using an SNOPT optimization algorithm based on the gradient;
and SS7, judging whether the SNOPT optimization algorithm is converged, if the SNOPT optimization algorithm is not converged, taking the new geometric design variable value obtained by optimizing in the step SS6 as a new basic sample point, repeating the steps SS 2-SS 6, and returning an optimization result after the SNOPT optimization algorithm is converged.
2. The method for robust optimization design of aircraft based on gradient-enhanced stochastic Co-Kriging model according to claim 1, wherein in the step SS1, the deterministic aerodynamic design conditions include at least Reynolds numberNumber of digitsReMach numberMaAngle of attack for airflowαThe design variables include at least geometric design variables and aerodynamic design variables including an uncertainty amount, the aerodynamic design variables include at least Mach numbersMaAngle of attack of air flowαThe constraints at least comprise geometric constraints and pneumatic constraints.
3. The method for robust optimization design of an aircraft based on a gradient-enhanced stochastic Co-Kriging model according to claim 1, wherein in the step SS2, the FFD geometric parameterization method adopts a bezier curve-based FFD method to flexibly control the aerodynamic profile of the aircraft or its aerodynamic components and reduce the number of control points and design variables required.
4. The method for designing an aircraft with robust optimization based on a gradient-enhanced stochastic Co-Kriging model according to claim 1, wherein in the step SS2, the IDW dynamic grid technique is an IDW method based on a local coordinate system, so as to maintain grid quality and orthogonality and avoid grid overlap and grid degradation.
5. The method for robust optimization design of an aircraft based on a gradient-enhanced stochastic Co-Kriging model according to claim 1, wherein in the step SS2, the grid set includes at least a surface grid and a volume grid, and the surface grid and the volume grid each adopt a structured grid, an unstructured grid or a hybrid grid to adapt to different flow field characteristics and calculation requirements.
6. The robust optimization design method of an aircraft based on a gradient-enhanced stochastic Co-Kriging model according to claim 1, wherein in the step SS3, for the basic sample points, the pneumatic design variables including the uncertainty amount are sampled in the stochastic space by using a uniform latin hypercube method, which adopts an optimization algorithm based on a maximum minimum distance criterion, improves uniformity and representativeness of the sampling points by maximizing minimum distances between the sampling points, and avoids aggregation and vacancy phenomena of the sampling points.
7. The method of claim 1, wherein in step SS3, the geometric design variable in each of the extended sample points comprises at least FFD control points, and the uncertainty pneumatic design variable comprises at least mach numberMaAngle of attack of air flowα。
8. The method for robust optimization design of an aircraft based on a gradient-enhanced stochastic Co-Kriging model according to claim 1, wherein in the step SS4, the pneumatic coupling adjoint method adopts a discrete adjoint equation, and uses a reynolds average numerical model to simulate a control equation and a discrete format of a solver.
9. The method according to claim 1, wherein in the step SS4, the aerodynamic characteristics include at least a lift coefficient, a drag coefficient, and a moment coefficient, and the gradient information of the aerodynamic characteristics to the geometric design variables includes at least a gradient of the lift coefficient to the FFD control point coordinates, a gradient of the drag coefficient to the FFD control point coordinates, and a gradient of the moment coefficient to the FFD control point coordinates, and the moment coefficient includes at least a roll moment, a pitch moment, and a yaw moment.
10. The method for robust optimization design of an aircraft based on a gradient-enhanced stochastic Co-Kriging model according to claim 1, wherein in the substep SS55, the unbiased condition based on the gradient-enhanced stochastic Co-Kriging model is:
（10）。
11. the method for robust optimization design of an aircraft based on a gradient-enhanced stochastic Co-Kriging model according to claim 10, wherein the formulas (7) and (8) are brought into formula (10), and the unbiased condition is obtained as follows:
（11）
wherein,，
，
。
12. the method for robust optimization design of an aircraft based on a gradient-enhanced stochastic Co-Kriging model of claim 11, wherein equation (11) is reduced to:
（12）
wherein the vector isComprises->A synergistic kriging coefficient->Is thatA matrix.
13. The method for robust optimization design of aircraft based on gradient-enhanced stochastic Co-Kriging model according to claim 1, wherein in the sub-step SS55, the variance of Co-Kriging error estimates is:
and the following symbols are introduced to simplify covariance:
（13）
the variance of the Co-Kriging error estimate written in matrix notation is obtained as follows:
（14）
wherein,is the covariance matrix Jin Xie in the covariance, consisting of the Kriging covariance matrix, the covariance between the primary and secondary responses, and the cross covariance matrix between the secondary responses, using the symbols introduced in equation (13), these matrices are defined as:
。
14. the method for designing the aircraft robust optimization based on the gradient-enhanced stochastic Co-Kriging model according to claim 1, wherein in the step SS6, the SNOPT optimization algorithm adopts a method based on sequence quadratic programming, utilizes gradient information provided by the gradient-enhanced stochastic Co-Kriging model to construct a quadratic programming sub-problem, and utilizes a trust domain strategy to control the scale and the solving precision of the sub-problem.
15. The method for robust optimization design of aircraft based on gradient-enhanced stochastic Co-Kriging model according to claim 1, wherein in the step SS6, the aerodynamic statistical momentDFor the target aerodynamic coefficientCThe mathematical expression of the linear combination of the mean and the standard deviation is as follows:
wherein,Kis a weight factor.
CN202311341946.XA 2023-10-17 2023-10-17 Aircraft robust optimization design method based on gradient enhancement random Co-Kriging model Active CN117077298B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202311341946.XA CN117077298B (en) 2023-10-17 2023-10-17 Aircraft robust optimization design method based on gradient enhancement random Co-Kriging model

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202311341946.XA CN117077298B (en) 2023-10-17 2023-10-17 Aircraft robust optimization design method based on gradient enhancement random Co-Kriging model

Publications (2)

Publication Number Publication Date
CN117077298A CN117077298A (en) 2023-11-17
CN117077298B true CN117077298B (en) 2023-12-29

Family

ID=88710169

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202311341946.XA Active CN117077298B (en) 2023-10-17 2023-10-17 Aircraft robust optimization design method based on gradient enhancement random Co-Kriging model

Country Status (1)

Country Link
CN (1) CN117077298B (en)

Citations (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108491668A (en) * 2018-04-17 2018-09-04 北京理工大学 A kind of aerocraft system optimization method based on the fusion of dynamic multi-model
CN109460566A (en) * 2018-09-20 2019-03-12 中国科学院工程热物理研究所 A kind of pneumatic Robust Optimal Design method of pneumatic equipment bladess inside thick wing type
CN111597698A (en) * 2020-05-08 2020-08-28 浙江大学 Method for realizing pneumatic optimization design based on deep learning multi-precision optimization algorithm
CN113657045A (en) * 2021-08-10 2021-11-16 北京理工大学 Complex aircraft model reduced order representation method based on multilayer cooperative Gaussian process
WO2022188001A1 (en) * 2021-03-08 2022-09-15 浙江大学 Reliability-based topology optimization design method for part structure by considering bounded hybrid uncertainty
WO2022188002A1 (en) * 2021-03-08 2022-09-15 浙江大学 Topology and material collaborative robust optimization design method for support structure using composite material
CN115525980A (en) * 2022-11-04 2022-12-27 北京航空航天大学 Optimization method and optimization device for aerodynamic configuration of reentry vehicle
CN116305523A (en) * 2023-01-09 2023-06-23 西安交通大学 Laminar flow airfoil optimization method based on discrete accompaniment
CN116341097A (en) * 2022-02-07 2023-06-27 西北工业大学 Transonic wing optimal design method based on novel high-dimensional proxy model
CN116822214A (en) * 2023-06-30 2023-09-29 南京航空航天大学 Multi-credibility data fusion method based on heteroscedastic Gaussian process regression

Patent Citations (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108491668A (en) * 2018-04-17 2018-09-04 北京理工大学 A kind of aerocraft system optimization method based on the fusion of dynamic multi-model
CN109460566A (en) * 2018-09-20 2019-03-12 中国科学院工程热物理研究所 A kind of pneumatic Robust Optimal Design method of pneumatic equipment bladess inside thick wing type
CN111597698A (en) * 2020-05-08 2020-08-28 浙江大学 Method for realizing pneumatic optimization design based on deep learning multi-precision optimization algorithm
WO2022188001A1 (en) * 2021-03-08 2022-09-15 浙江大学 Reliability-based topology optimization design method for part structure by considering bounded hybrid uncertainty
WO2022188002A1 (en) * 2021-03-08 2022-09-15 浙江大学 Topology and material collaborative robust optimization design method for support structure using composite material
CN113657045A (en) * 2021-08-10 2021-11-16 北京理工大学 Complex aircraft model reduced order representation method based on multilayer cooperative Gaussian process
CN116341097A (en) * 2022-02-07 2023-06-27 西北工业大学 Transonic wing optimal design method based on novel high-dimensional proxy model
CN115525980A (en) * 2022-11-04 2022-12-27 北京航空航天大学 Optimization method and optimization device for aerodynamic configuration of reentry vehicle
CN116305523A (en) * 2023-01-09 2023-06-23 西安交通大学 Laminar flow airfoil optimization method based on discrete accompaniment
CN116822214A (en) * 2023-06-30 2023-09-29 南京航空航天大学 Multi-credibility data fusion method based on heteroscedastic Gaussian process regression

Non-Patent Citations (7)

* Cited by examiner, † Cited by third party
Title
Co-Kriging Based Multi-fidelity Aerodynamic Optimization for Flying Wing UAV with Multi-shape Wingtip Design;Ruochen Wang 等;《2021 IEEE International Conference on Unmanned Systems (ICUS)》》;全文 *
基于代理模型的高效全局气动优化设计方法研究进展;韩忠华 等;《航空学报》;第41卷(第5期);全文 *
基于自适应多可信度多项式混沌-Kriging 模型的高效气动优化方法;赵欢;《力学学报》;第55卷(第1期);全文 *
带下表面射流的超临界翼型优化;戴雅雪 等;《工程力学》;全文 *
民用客机机翼/机身/平尾构型气动外形优化设计;陈颂;白俊强;史亚云;乔磊;;航空学报(10);全文 *
湍流工况小型风力机翼型气动特性及稳健优化;唐新姿;李鹏程;彭锐涛;陆鑫宇;;机械工程学报(02);全文 *
自由变形技术在RAE2822翼型优化设计中的应用;陈立立;郭正;侯中喜;;国防科技大学学报(05);全文 *

Also Published As

Publication number Publication date
CN117077298A (en) 2023-11-17

Similar Documents

Publication Publication Date Title
Zheng et al. A hybrid variable-fidelity global approximation modelling method combining tuned radial basis function base and kriging correction
CN105718634B (en) A kind of aerofoil profile Robust Optimal Design based on non-probability interval analysis model
Gang et al. Mesh deformation on 3D complex configurations using multistep radial basis functions interpolation
CN114065662B (en) Method suitable for rapidly predicting airfoil flow field with variable grid topology
Seshadri et al. A density-matching approach for optimization under uncertainty
Cordero-Gracia et al. An interpolation tool for aerodynamic mesh deformation problems based on octree decomposition
Leifsson et al. Optimal shape design of multi-element trawl-doors using local surrogate models
CN115688276A (en) Aircraft appearance automatic optimization method, system, equipment and medium based on discrete companion method
CN115438598A (en) Numerical method of Reynolds stress turbulence model based on general time root square scale
Malouin et al. Interpolation of transonic flows using a proper orthogonal decomposition method
Amrit et al. Design strategies for multi-objective optimization of aerodynamic surfaces
Yi et al. Efficient global optimization using a multi-point and multi-objective infill sampling criteria
Xiong et al. A point cloud deep neural network metamodel method for aerodynamic prediction
Palar et al. Decomposition-based evolutionary aerodynamic robust optimization with multi-fidelity point collocation non-intrusive polynomial chaos
CN117077298B (en) Aircraft robust optimization design method based on gradient enhancement random Co-Kriging model
Leifsson et al. Variable-resolution shape optimisation: Low-fidelity model selection and scalability
Quagliarella et al. An open-source aerodynamic framework for benchmarking multi-fidelity methods
Meng et al. A nurbs-enhanced finite volume method for steady euler equations with goal-oriented h-adaptivity
Piperni et al. Singlepoint and multipoint robust design of airfoils using CST functions
CN108197368B (en) Method for simply and conveniently calculating geometric constraint and weight function of complex aerodynamic shape of aircraft
Selvan On the effect of shape parameterization on aerofoil shape optimization
CN109033678A (en) A kind of aircraft near-optimal design method generated based on virtual sample
Clarich et al. A Competitive Game Approach for Multi Objective Robust Design Optimization
Buccafusca et al. Maximizing power in wind turbine arrays with variable wind dynamics
Ko et al. Finite macro‐element‐based volume grid deformation for large moving boundary problems

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant